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A ceramic specimen with an elastic modulus of 300 GPa is under a tensile stress of 800 MPa. Will it fracture if its most severe flaw is an internal crack of 0.30 mm long with a tip radius of curvature in the amount of 0.0015 mm? Please justify your conclusion. (Hint: Compare the largest stress in the specimen around the crack to the theoretical strength which is roughly E/10).

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ogorwyne

Answer:

16Gpa < 30 Gpa

there would be no fracture

Explanation:

fracture can occur if the maximum strength at the top of the biggest flaw is more than the theoretical fracture

to get the theoretical strength =

e/10 = 300/10

= 30 Gpa

we get the magnitude at the buggest flaw

= 2σ√a/ρt

σ = 800

ρτ = 0.0015

a= 0.3/2

[tex]=2*800\sqrt{\frac{\frac{0.3}{2} }{0.0015} }[/tex]

= [tex]=2*800*\sqrt{100} \\=2*800*10\\=16000MPa[/tex]

= 16Gpa < 30 Gpa

the fracture is not going to happen given that the maximum strenght is smaller than the theoretical fracture strength.

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